Cvx algorithm for mosek

1

I tried formulating my problem to mosek directly.

It took my code to setup the problem 10 seconds more than cvx.
cvx eliminated 3/5 of the constraints.
After factorization cvx had 2.9e5 nnz vs. 1.4e8 nnz in mine.
This leads to mosek solution of 1.3 seconds for cvx formulation, while for my formulation I stopped it on the fourth iteration after 183 seconds.

I should note that mosek eliminated variables for my formulation, which means that cvx does a better job at it.

How do you do it?

2

One thing that CVX does that MOSEK does not is to dualize when it thinks it is wortwhile.
So maybe CVX is feeding MOSEK with dual problem. It seems I am correct. See the Yalmip post.

3

Yes, we should continue the discussion on the other thread. Although it’s not the same, it’s a very similar problem (2D vs 3D).

4

Looking at the linked thread, it is clear Erling is correct. CVX passes the solver the dual problem whenever its heuristics suggest that doing so would be more efficient.